how to solve for radius of horizontal curve with coordinates(NE) for points A,B, C on the curve
By horizontal curve, I suppose you mean an arc and not a spiral.
When three points A,B and C are given in order of chainage, you can find the radius first by finding the centre O, which in turn is at the intersection of any two diameters. You can find two diameters as the perpendicular bisectors of chords AB and BC.
Finally, the radius is the distance between O and A (or B, or C). Do check your calculations by finding the distances OA, OB and OC.
If you need help in finding the line along perpendicular bisector between two given points A(xa,ya) and B(xb,yb), here it is:
1. Find the line passing through AB.
2. calculate the slope the the preceding line, m.
3. find the mid-point D between A and B.
4. the perpendicular bisector is the line passing through D with a slope of -1/m.
kinda lost maybe help if gave more information,
Point A : N1405.4018
E1256.7569
Point B : N1283.3703
E1294.7027
Point C : N1225.9373
E1286.6137
Could please explain one more time, thank you
To solve for the radius of a horizontal curve with coordinates (NE) for points A, B, and C on the curve, you will need the following steps:
1. Identify the coordinates of points A, B, and C on the curve (NE). Let's assume the coordinates are (xA, yA), (xB, yB), and (xC, yC), respectively.
2. Calculate the change in x and y coordinates between points A and B, and between points B and C. The change in x (Δx) is calculated as Δx = xB - xA, and the change in y (Δy) is calculated as Δy = yB - yA for AB, and Δx = xC - xB and Δy = yC - yB for BC.
3. Determine the distance between points A and B (AB) and between points B and C (BC). The distance is given by the formula d = sqrt(Δx^2 + Δy^2). Calculate AB as AB = sqrt(Δx_AB^2 + Δy_AB^2), and BC as BC = sqrt(Δx_BC^2 + Δy_BC^2).
4. Calculate the tangent of the angle of deflection between AB and BC. The tangent is given by the formula tanθ = Δy_BC / Δx_BC.
5. Determine the central angle (θ) between AB and BC using the tangent value from step 4. The central angle can be calculated as θ = arctan(tanθ).
6. Calculate the chord length (C) using the distance formulas from step 3. For AB, C = AB / 2, and for BC, C = BC / 2.
7. Calculate the radius of the horizontal curve (R) using the chord length (C) and the central angle (θ) using the formula R = C / sin(θ / 2).
By following these steps, you can solve for the radius of a horizontal curve with coordinates (NE) for points A, B, and C on the curve.